Question

multiple choice 0.5 points
which interval has the largest magnitude of average velocity?
table 2.1 position of
the car at various times
position t (s) x (m)
a 0 30
b 10 52
c 20 38
d 30 0
e 40 -37
f 50 -53
d to e
e to f
c to d
a to b

Explanation:

Step1: Recall average velocity formula

Average velocity: $v_{avg} = \frac{\Delta x}{\Delta t} = \frac{x_f - x_i}{t_f - t_i}$, magnitude is $|v_{avg}|$

Step2: Calculate A to B magnitude

$\Delta t = 10-0=10\ \text{s}$, $\Delta x=52-30=22\ \text{m}$
$|v_{avg}| = \frac{22}{10} = 2.2\ \text{m/s}$

Step3: Calculate C to D magnitude

$\Delta t = 30-20=10\ \text{s}$, $\Delta x=0-38=-38\ \text{m}$
$|v_{avg}| = \frac{|-38|}{10} = 3.8\ \text{m/s}$

Step4: Calculate D to E magnitude

$\Delta t = 40-30=10\ \text{s}$, $\Delta x=-37-0=-37\ \text{m}$
$|v_{avg}| = \frac{|-37|}{10} = 3.7\ \text{m/s}$

Step5: Calculate E to F magnitude

$\Delta t = 50-40=10\ \text{s}$, $\Delta x=-53-(-37)=-16\ \text{m}$
$|v_{avg}| = \frac{|-16|}{10} = 1.6\ \text{m/s}$

Step6: Compare all magnitudes

$3.8 > 3.7 > 2.2 > 1.6$

Answer:

C. C to D